Once a complete model is created, the user can simulate the model to update the state of the structure. For diffusion simulation, a -transientSolve is usually performed for a certain time interval. A -staticSolve is also available for solving elliptic systems of PDEs.
The default timestepping algorithm for -transientSolve is
TR/BDF2. The timestepping algorithm can be changed using
-timeIntegrator algorithm. The algorithms that are currently
available are TRBDF2 (second-order accurate, A-stable,
L-stable, not monotonic), backwardEuler (generalized
trapezoid with 
, first-order accurate, A-stable,
L-stable, monotonic?), implicitEuler (generalized trapezoid
with 
, first-order accurate, conditionally A-stable),
and trapezoidalRule (generalized trapezoid with 
, second-order accurate, A-stable, not L-stable, not
monotonic).